Astronaut Acceleration Question

[shell4987]

Homework Statement

Three astronauts, propelled by jet backpacks, push and guide a 160 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-31, with F1 = 30 N, F2 = 36 N, F3 = 58 N, 1 = 27°, and 3 = 55°. What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction relative to the positive direction of the x axis?? (give the magnitude of the angle)

Homework Equations

F=ma

The Attempt at a Solution

I don't really know where to start on this problem, do I just use the F=ma formula for each force and solve for a? How can I put it in unit vector notation?

 

[mgb_phys]

Apply F = ma in each coordinate separately
Simply use pythagorus to get the overall magnitude ( no diagram I assume the directions are in x,y,z?)
To get the overal direction just draw a force diagram and do the trig.

 

[m2003]

As a scientist, you are correct in thinking that you can use the formula F=ma to solve for the asteroid's acceleration in this scenario. However, in order to put it in unit vector notation, you will need to break down the forces into their x and y components. To do this, you can use trigonometry and the given angles to determine the x and y components of each force. Once you have the x and y components, you can add them together to find the net force in each direction. Then, you can use the formula F=ma to solve for the acceleration in each direction. Finally, you can express the acceleration in unit vector notation by dividing the acceleration in each direction by the magnitude of the net force. This will give you the unit vector notation for the acceleration (a = <ax, ay>).

To find the magnitude of the acceleration, you can use the Pythagorean theorem to find the net force and then use F=ma to solve for the acceleration. To find the direction of the acceleration, you can use inverse trigonometric functions to solve for the angle of the net force. This angle will be the direction of the acceleration relative to the positive direction of the x axis.

I hope this helps guide you in solving this problem. Remember to always break down forces into their components and use the appropriate formulas to solve for the desired values.